SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class ExponentialDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.ExponentialDist
```
All Implemented Interfaces:
Distribution
Direct Known Subclasses:
ExponentialDistFromMean

`public class ExponentialDistextends ContinuousDistribution`

Extends the class `ContinuousDistribution` for the exponential distribution with mean 1/λ where λ > 0. Its density is

f (x) = λe-λx        for x >= 0,

its distribution function is

F(x) = 1 - e-λx,        for x >= 0,

and its inverse distribution function is

F-1(u) = - ln(1 - u)/λ,        for 0 < u < 1.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`decPrec`

Constructor Summary
`ExponentialDist()`
Constructs an ExponentialDist object with parameter λ = 1.
`ExponentialDist(double lambda)`
Constructs an ExponentialDist object with parameter λ = lambda.

Method Summary
` double` `barF(double x)`
Returns the complementary distribution function.
`static double` ```barF(double lambda, double x)```
Computes the complementary distribution function.
` double` `cdf(double x)`
Returns the distribution function F(x).
`static double` ```cdf(double lambda, double x)```
Computes the distribution function.
` double` `density(double x)`
Returns f (x), the density evaluated at x.
`static double` ```density(double lambda, double x)```
Computes the density function.
`static ExponentialDist` ```getInstanceFromMLE(double[] x, int n)```
Creates a new instance of an exponential distribution with parameter λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
` double` `getLambda()`
Returns the value of λ for this object.
` double` `getMean()`
Returns the mean.
`static double` `getMean(double lambda)`
Computes and returns the mean, E[X] = 1/λ, of the exponential distribution with parameter λ.
`static double[]` ```getMLE(double[] x, int n)```
Estimates the parameter λ of the exponential distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
` double[]` `getParams()`
Return a table containing the parameters of the current distribution.
` double` `getStandardDeviation()`
Returns the standard deviation.
`static double` `getStandardDeviation(double lambda)`
Computes and returns the standard deviation of the exponential distribution with parameter λ.
` double` `getVariance()`
Returns the variance.
`static double` `getVariance(double lambda)`
Computes and returns the variance, Var[X] = 1/λ2, of the exponential distribution with parameter λ.
` double` `inverseF(double u)`
Returns the inverse distribution function x = F-1(u).
`static double` ```inverseF(double lambda, double u)```
Computes the inverse distribution function.
` void` `setLambda(double lambda)`
Sets the value of λ for this object.
` String` `toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### ExponentialDist

`public ExponentialDist()`
Constructs an ExponentialDist object with parameter λ = 1.

### ExponentialDist

`public ExponentialDist(double lambda)`
Constructs an ExponentialDist object with parameter λ = lambda.

Method Detail

### density

`public double density(double x)`
Description copied from class: `ContinuousDistribution`
Returns f (x), the density evaluated at x.

Specified by:
`density` in class `ContinuousDistribution`
Parameters:
`x` - value at which the density is evaluated
Returns:
density function evaluated at x

### cdf

`public double cdf(double x)`
Description copied from interface: `Distribution`
Returns the distribution function F(x).

Parameters:
`x` - value at which the distribution function is evaluated
Returns:
distribution function evaluated at x

### barF

`public double barF(double x)`
Description copied from class: `ContinuousDistribution`
Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:
`barF` in interface `Distribution`
Overrides:
`barF` in class `ContinuousDistribution`
Parameters:
`x` - value at which the complementary distribution function is evaluated
Returns:
complementary distribution function evaluated at x

### inverseF

`public double inverseF(double u)`
Description copied from class: `ContinuousDistribution`
Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].

Specified by:
`inverseF` in interface `Distribution`
Overrides:
`inverseF` in class `ContinuousDistribution`
Parameters:
`u` - value at which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

### getMean

`public double getMean()`
Description copied from class: `ContinuousDistribution`
Returns the mean.

Specified by:
`getMean` in interface `Distribution`
Overrides:
`getMean` in class `ContinuousDistribution`
Returns:
the mean

### getVariance

`public double getVariance()`
Description copied from class: `ContinuousDistribution`
Returns the variance.

Specified by:
`getVariance` in interface `Distribution`
Overrides:
`getVariance` in class `ContinuousDistribution`
Returns:
the variance

### getStandardDeviation

`public double getStandardDeviation()`
Description copied from class: `ContinuousDistribution`
Returns the standard deviation.

Specified by:
`getStandardDeviation` in interface `Distribution`
Overrides:
`getStandardDeviation` in class `ContinuousDistribution`
Returns:
the standard deviation

### density

```public static double density(double lambda,
double x)```
Computes the density function.

### cdf

```public static double cdf(double lambda,
double x)```
Computes the distribution function.

### barF

```public static double barF(double lambda,
double x)```
Computes the complementary distribution function.

### inverseF

```public static double inverseF(double lambda,
double u)```
Computes the inverse distribution function.

### getMLE

```public static double[] getMLE(double[] x,
int n)```
Estimates the parameter λ of the exponential distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimate is returned in a one-element array, as element 0.

Parameters:
`x` - the list of observations used to evaluate parameters
`n` - the number of observations used to evaluate parameters
Returns:
returns the parameter [ hat(λ)]

### getInstanceFromMLE

```public static ExponentialDist getInstanceFromMLE(double[] x,
int n)```
Creates a new instance of an exponential distribution with parameter λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.

Parameters:
`x` - the list of observations to use to evaluate parameters
`n` - the number of observations to use to evaluate parameters

### getMean

`public static double getMean(double lambda)`
Computes and returns the mean, E[X] = 1/λ, of the exponential distribution with parameter λ.

Returns:
the mean of the exponential distribution E[X] = 1/λ

### getVariance

`public static double getVariance(double lambda)`
Computes and returns the variance, Var[X] = 1/λ2, of the exponential distribution with parameter λ.

Returns:
the variance of the Exponential distribution Var[X] = 1/λ2

### getStandardDeviation

`public static double getStandardDeviation(double lambda)`
Computes and returns the standard deviation of the exponential distribution with parameter λ.

Returns:
the standard deviation of the exponential distribution

### getLambda

`public double getLambda()`
Returns the value of λ for this object.

### setLambda

`public void setLambda(double lambda)`
Sets the value of λ for this object.

### getParams

`public double[] getParams()`
Return a table containing the parameters of the current distribution.

### toString

`public String toString()`
Overrides:
`toString` in class `Object`

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.